chore: improve the implementation of `math/base/special/hyp2f1` by officiallyanee · Pull Request #11325 · stdlib-js/stdlib

officiallyanee · 2026-04-07T22:10:38Z

type: pre_commit_static_analysis_report
description: Results of running static analysis checks when committing changes. report:

task: lint_filenames status: passed
task: lint_editorconfig status: passed
task: lint_markdown status: na
task: lint_package_json status: na
task: lint_repl_help status: na
task: lint_javascript_src status: passed
task: lint_javascript_cli status: na
task: lint_javascript_examples status: na
task: lint_javascript_tests status: passed
task: lint_javascript_benchmarks status: na
task: lint_python status: missing_dependencies
task: lint_r status: na
task: lint_c_src status: na
task: lint_c_examples status: na
task: lint_c_benchmarks status: na
task: lint_c_tests_fixtures status: na
task: lint_shell status: na
task: lint_typescript_declarations status: passed
task: lint_typescript_tests status: na
task: lint_license_headers status: passed ---

Resolves none.

Description

What is the purpose of this pull request?

This pull request:

This pull request improves the JS implementation of math/base/special/hyp2f1. It started with this issue:

which is now

Though the difference still exists but wolfram gives 0.0040689094468919286...
so output now is closer to wolfram.
It also uses some updated implementation from scipy's cephes hyp2f1 with added test cases to test the same.
I will work on C implementation once this gets the green light.

Related Issues

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This pull request has the following related issues:

None

Questions

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No.

Other

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No.

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Please ensure the following tasks are completed before submitting this pull request.

Read, understood, and followed the contributing guidelines.

AI Assistance

When authoring the changes proposed in this PR, did you use any kind of AI assistance?

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Code generation (e.g., when writing an implementation or fixing a bug)
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Research and understanding

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If you answered "yes" to using AI assistance, please provide a short disclosure indicating how you used AI assistance. This helps reviewers determine how much scrutiny to apply when reviewing your contribution. Example disclosures: "This PR was written primarily by Claude Code." or "I consulted ChatGPT to understand the codebase, but the proposed changes were fully authored manually by myself.".

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--- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: na - task: lint_python status: missing_dependencies - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed ---

stdlib-bot · 2026-04-07T22:13:12Z

Coverage Report

Package	Statements	Branches	Functions	Lines
math/base/special/hyp2f1	$\color{red}1001/1069$ $\color{green}+93.64%$	$\color{red}119/130$ $\color{green}+91.54%$	$\color{green}8/8$ $\color{green}+100.00%$	$\color{red}1001/1069$ $\color{green}+93.64%$

The above coverage report was generated for the changes in this PR.

officiallyanee · 2026-04-07T22:32:39Z

lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/hyt2f1.js

+			if ( id > 0.0 ) {
+				y *= q;
+			} else {
+				y1 *= q;
+			}


This was wrong originally, cephes and scipy both have this but it was not discovered probably because else branch is never hit ( in test cov ) so I changed it.

To clarify, the bug was in y1 *= q mistakenly being implemented as y = y1 * q, correct?

Yes, the snippet from cephes for reference:

if( id > 0.0 ) y *= q; else y1 *= q; y += y1;

officiallyanee · 2026-04-07T22:33:57Z

lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/main.js

+// FUNCTIONS //
+
+/**
+* Evaluates 2F1(a, b; b; x) when `b = c` is a negative integer using AMS55 #15.4.2.
+*
+* @private
+* @param {number} a - first parameter
+* @param {number} b - second parameter (equals c, a non-positive integer)
+* @param {number} x - argument
+* @returns {number} function value, or NaN if precision is insufficient
+*/
+function hyp2f1NegCEqualBC( a, b, x ) {
+	var collectorMax;
+	var collector;
+	var sum;
+	var k;
+
+	if ( !( abs( b ) < 1.0e5 ) ) {
+		return NaN;
+	}
+	collectorMax = 1.0;
+	collector = 1.0;
+	sum = 1.0;
+	for ( k = 1; k <= -b; k++ ) {
+		collector *= ( a + k - 1.0 ) * x / k;
+		collectorMax = max( abs( collector ), collectorMax );
+		sum += collector;
+	}
+	if ( 1.0e-16 * ( 1.0 + ( collectorMax / abs( sum ) ) ) > 1.0e-7 ) {
+		return NaN;
+	}
+	return sum;
+}
+
+


I will add this in a separate file if that would be better, the implementation for this was taken from scipy.

Yes, if you don't mind going ahead and moving. Cheers!

officiallyanee · 2026-04-07T22:36:23Z

lib/node_modules/@stdlib/math/base/special/hyp2f1/lib/hyt2f1.js

 	id = round( d );

-	if ( x > 0.9 && !negIntA && !negIntB ) {
+	if ( x > 0.85 && !negIntA && !negIntB ) {


0.85 was chosen arbitrarily through trial and error, this helped the case I mentioned in the description.

@officiallyanee Do you happen to know where/why the 0.9 was chosen in the first place?

Its not explicitly mentioned in the cephes/scipy code but I went through some resources and found this:

ref: https://link.springer.com/article/10.1007/s11075-016-0173-0
I think it also explains why the initial case was performing badly too since |a| and |b| were much larger than |c|
and |x| is also pretty close to 1 so the power series was performing poorly.
In the range 0.85<x<0.9, it was true for every value as long as we keep a, b, c same.
( this is assuming wolfram as a better source of comparision )

kgryte · 2026-04-09T07:55:08Z

/stdlib merge

kgryte · 2026-04-09T07:59:45Z

lib/node_modules/@stdlib/math/base/special/hyp2f1/test/test.js

+	for ( i = 0; i < x.length; i++ ) {
+		v = hyp2f1( a[ i ], b[ i ], c[ i ], x[ i ] );
+		delta = abs( v - expected[ i ] );
+		tol = 8.0 * EPS * abs( expected[ i ] );


We just had another PR land which migrated hyp2f1 to use ULP-based testing. If you could follow suit here, that would be appreciated!

kgryte · 2026-04-10T05:58:11Z

/stdlib merge

kgryte · 2026-04-10T06:15:28Z

@officiallyanee Merged in the latest develop, which should have the test fixes.

stdlib-bot added Math Issue or pull request specific to math functionality. Needs Review A pull request which needs code review. labels Apr 7, 2026

officiallyanee commented Apr 7, 2026

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github-actions bot mentioned this pull request Apr 8, 2026

[aw] No-Op Runs #11033

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stdlib-bot added the bot: In Progress Pull request is currently awaiting automation. label Apr 9, 2026

Merge remote-tracking branch 'upstream/develop' into improve/hyp2f1

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stdlib-bot removed the bot: In Progress Pull request is currently awaiting automation. label Apr 9, 2026

kgryte reviewed Apr 9, 2026

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kgryte added Needs Changes Pull request which needs changes before being merged. and removed Needs Review A pull request which needs code review. labels Apr 9, 2026

stdlib-bot added the bot: In Progress Pull request is currently awaiting automation. label Apr 10, 2026

Merge remote-tracking branch 'upstream/develop' into improve/hyp2f1

cc3d8a1

stdlib-bot removed the bot: In Progress Pull request is currently awaiting automation. label Apr 10, 2026

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officiallyanee Apr 7, 2026 • edited Loading Uh oh! There was an error while loading. Please reload this page.

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kgryte commented Apr 9, 2026

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kgryte commented Apr 10, 2026

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officiallyanee commented Apr 7, 2026 •

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